I just came to this note
For any LTI system the transfer function is W(s)=X(s)/F(s)
e.g for the system x' + 3x = f(t),
the transfer function is W=1/3+s
but this system has a term f(t) dependent on t so it shouldn't be autonomous, right?
Is this equation time-invariant and autonomous?
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ordinary-differential-equations
control-theory
invariance
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0Yes, maybe that is easier to see if you write the vector field as $\dot{x}(t)=f(t)-3x(t)=F(x(t),t)$. – 2017-01-26
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0then it's not autonomous?? https://en.wikipedia.org/wiki/Autonomous_system_(mathematics) – 2017-01-26
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0I responded on your last question, sorry for the confusion. – 2017-01-26
1 Answers
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Your system is time-invariant since the parameters (e.g. the number 3 that multiplies the x) do not depend on time. The variables (x,f) can depend on time.